"What happened is appalling and justice should be swift," Ryan said of the Friday incident, in which Robert Dear Jr. allegedly opened fire at the clinic and killed three people. “Clearly we can do more, and one common denominator in these tragedies is mental illness.”

Ryan and his leadership team are backing legislation by Rep. Tim Murphy (R-Pa.), a longtime psychologist, that would overhaul the mental healthcare system, especially focusing on helping people with serious mental illness. It would create a new assistant secretary for mental health and removes restrictions on Medicaid paying for certain mental healthcare.

The Murphy bill currently is working its way through the Energy and Commerce Committee.

“I'm sure members of both parties have lots of ideas in this area,” the Speaker said, “but we should make this a priority to prevent the violence and to protect our citizens.”

Some Democrats, however, have warned that the Murphy bill could lower privacy protections by allowing more treatment information to be shared with caregivers. They also object to financial incentives for states to allow judges to mandate treatment for certain people with serious mental health issues.

On the gun-reform front, the Democrats appear poised to focus on legislation that would block those on the government's terrorist watch-list from buying or owning firearms — a prohibition not currently in place.